Find the remainder when \(3x^{3}-4x^{2}+2x-5\) is divided by \(x-2\).

Step 1 ：Step 1: Write the dividend and the divisor in long division format. We are looking for the quotient and the remainder when dividing \(3x^{3} -4x^{2} +2x - 5\) by \(x - 2\).

Step 2 ：Step 2: Divide the first term of the dividend by the first term of the divisor, that is, \(\frac{3x^{3}}{x} = 3x^{2}\). Write this term above the division bar.

Step 3 ：Step 3: Multiply the divisor \(x - 2\) by the term \(3x^{2}\) obtained in Step 2 and subtract this from the original dividend to obtain a new dividend.

Step 4 ：Step 4: Repeat the process with the new dividend. Divide \(-2x^{2}\) by \(x\) to get \(-2x\), write it above the division bar, and subtract \(-2x*(x-2)\) from the new dividend.

Step 5 ：Step 5: Repeat the process with the new dividend. Divide \(6x\) by \(x\) to get \(6\), write it above the division bar, and subtract \(6*(x-2)\) from the new dividend.

Step 6 ：Step 6: Now we cannot proceed further as the degree of the remaining dividend \(7\) is less than the degree of the divisor \(x - 2\). So, \(7\) is the remainder when \(3x^{3} - 4x^{2} + 2x - 5\) is divided by \(x - 2\).